Displacement of COM:Application

Q.

A child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u, the centre of mass of the system (trolley + child) will move with a speed

1. Zero

2. (v + u)

3. (v - u)

4. v

Q.

A mon of mass 'm' moves on a plank of mass 'M' with a constant velocity 'u' with respect to the plank (as shown in the figure). If the plank rests on a smooth horizontal surface, then determine the final velocity of the plank.

1. 

2. 

3. 

4. u

Q.

Why does a cricketer lower his hands while catching a ball?

Q.

The motion of centre of mass of a system of two particles is unaffected by their internal forces

1. irrespective of the actual direction of the internal forces.

2. only if they are along the line joining the particles.

3. only if they are at right angles to the line joining the particles.

4. only if they are obliquely inclined to the line joining the particles.

Q. Why are roads on mountain inclined inwards in turns?

Q. Two bodies of masses 3 kg and 12 kg are placed at a distance of 12 m. The third body of mass 0.5 kg is to be placed at such a point that the force acting on this body is zero. Find the position of that point.

Q.

A rod $AB$ of mass $10$$kg$ and length $4$ $m$ rests on a horizontal floor with end $A$ fixed so, as to rotate it in a vertical plane about a perpendicular axis passing through $A$. If the work done on the rod is $100$ $J$, the height to which the end $B$ be raised vertically above the floor is

1. $1.5m$

2. $2m$

3. $1m$

4. $2.5m$

5. $3m$

Q.

Why do paratroopers roll on landing?

Q. An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on the magnitude and direction of the velocity. If no, provide a reason.

Q. What is the difference between simple and compound pendulum?

Q. A soldier fires a bullet of mass 50 g with a velocity 100 m/S, then find the recoil speed of gun whose mass is 20 kg.

1. 25 m/s
2. 1 m/s
3. 10 m/s
4. 0.25 m/s

Q.

A loaded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation $\theta$. The gun is initially at rest on a horizontal frictionless surface. After firing, the centre of mass of the gun-shot system

1. remains at rest in the horizontal direction.

2. moves with a velocity $\frac{vm}{M}$ in the horizontal direction.

3. moves with velocity $\frac{vmcos\theta }{M}$ in the horizontal direction.

4. moves with a velocity $\frac{v(M-m)}{(M+m)}$ in the horizontal direction.

Q.

A force of 20N acts on a body whose weight is 9.8N. What is the mass of the body?

Q.

Does the centre of mass of a body necessarily lie inside the body ?

Q.

If a man of mass M jumps to the ground from a height h and his centre of mass moves a distance of x during the impact, the average force acting on him (assuming his retardation to be constant during his impact with the ground) is

1. $Mg{\left(\frac{h}{x}\right)}^2$

2. $Mg{\left(\frac{x}{h}\right)}^2$

3. $\frac{Mgh}{x}$

4. $\frac{Mgx}{h}$

Q.

A block of mass 'M' is placed on the top of a bigger inclined plane of mass '10M' as shown in figure. All the surfaces are frictionless. The system is released from rest. Find the distance moved by the bigger block at the instant the smaller block reaches the ground.

1. 0.2m

2. 0.4m

3. 0.1m

4. 0.3m

Q.

Inside a hollow uniform sphere of mass 'M', a uniform rod of lenght 'R$\sqrt{2}$' is released from the state of rest. The mass of the rod is same as that of the sphere. If the inner radius of the hollow sphere is 'R' then find out horizontal displacement of sphere with respect to earth in the time in which the rod becomes horizontal.

1. 
   

2. 

3. 

4. 

Q.

If a man of mass M jumps to the ground from a height h and his centre of mass moves a distance of x during the impact, the average force acting on him (assuming his retardation to be constant during his impact with the ground) is

1. $\frac{Mgh}{x}$

2. $\frac{Mgx}{h}$

3. $Mg{\left(\frac{h}{x}\right)}^2$

4. $Mg{\left(\frac{x}{h}\right)}^2$

Q. Three identical trolleys of sand, each of mass 10 kg, are being pulled by the labour as shown. If the pulling force (F) is 30N, then what is the acceleration of each trolley and what are the tensions acting on each rope? Assume no friction is acting on the trolleys.

1. a = 1 $m{s}^{-2}$; $T_1$ = 10 N; $T_2$ = 20 N
2. a = 2 $m{s}^{-2}$; $T_1$ = 10 N; $T_2$ = 20 N

3. a = 1 $m{s}^{-2}$; $T_1$ = 20 N; $T_2$ = 10 N

4. a = 2 $m{s}^{-2}$; $T_1$ = 20 N; $T_2$ = 10 N

Q. A cart of mass 'M' is at rest on a frictionless horizontal surface and a pendulum bob of mass 'm' hangs from the roof of the cart. The string breaks, the bob falls on the floor, makes several collisions on the floor and finally lands up in a small slot made on the floor. The horizontal distance between the string and the slot is 'L'. Find the displacement of the cart during this process.

1. $\frac{Ml}{M+m}$ to the right
2. $\frac{Ml}{M+m}$ to the left
3. $\frac{ml}{M+m}$ to the right
4. $\frac{ml}{M+m}$ to the left

Q. A stone is dropped on the moon from a height of $30m$. The acceleration due to gravity on the moon is $\frac{g}{6}$. Determine the approximate time taken by the stone to fall on the surface of the moon.
(Take $g=10m/s^2$ )

1. $2sec$
2. $3sec$
3. $5sec$
4. $6sec$

Q. Mr. Verma (50 kg) and Mr. Mathur (60 kg) are sitting at the two extremes of a 4 m long boat (40 kg) standing still in water. To discuss a mechanics problem, they come to the middle of the boat. Neglecting friction with water, how far does the boat move in the water during the process?

1. 2 m
2. 3/15 m
3. 2/15 m
4. 1/15 m

Q.

A cart of mass M is tied at one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. Initially, the man is at x = 0 and the cart at x = 10 m. If the man pulls the cart using the rope, the man and the cart will meet at the point

1. x = 0

2. x = 5 m

3. x = 10 m

4. They will never meet.

Q.

A cart of mass M is tied at one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. Initially, the man is at x = 0 and the cart at x = 10 m. If the man pulls the cart using the rope, the man and the cart will meet at the point

1. x = 0

2. x = 5 m

3. x = 10 m

4. They will never meet.

Q. Two balls A and B of equal masses are projected upward simultaneously, one from the ground with speed 50 $m{s}^{-1}$ and other from height 40 m above the first ball high tower with initial speed 30 $m{s}^{-1}$. Find the maximum height attained by their centre of mass.

1. 80 m
2. 20 m
3. 100 m
4. 60 m

Q. Two balls, A and B of masses 0.4 kg and 1.2 kg respectively, are placed at a distance of 12 cm from each other. Another ball of mass 0.1 kg is placed in between them such that there is no net force acting on it. Find the distance of the third ball from ball A.

1. $-6-6\sqrt{3}\text{cm}$
2. $-6+6\sqrt{3}\text{cm}$
3. $12-6\sqrt{3}\text{cm}$
4. $-12+6\sqrt{3}\text{cm}$

Q.

standing is not allowed in double decker bus. why?

Q. A 6 kg bomb at rest explodes into three pieces P , Q and R of equal mass.If P fly with speed 30 metre per second and Q with 40 metre per second perpendicular to each other find angle between P & R.

Q. From a rifle of mass 5 kg, a bullet of mass 100 g is fired with a velocity of 35 m$s^{-1}$ with respect to the ground. Calculate the recoil velocity of the rifle.

Q. $\text{A}.$ State the principle behind the working of a hydraulic machine and explain the working of hydraulic brakes. $\left[3\text{marks}\right]$


$\text{B}.\text{(i)}$ Write the equations of motion for a body that is being uniformly accelerated. $\left[1\text{mark}\right]$
$\text{(ii)}$ A car moving with a constant acceleration covers the $60\text{m}$ distance between two points
in $6\text{s}$. Its speed as it passes the second point was $15\text{m/s}.$
Find:(a) Its speed at the first point.
(b) Its acceleration.
(c) Its distance prior to the first point at which the body was at rest. $\left[2\text{marks}\right]$


$\text{C}.\text{(i)}$ State the universal law of gravitation.$\left[2\text{marks}\right]$
$\text{(ii)}$ Two identical blocks of mass $10\text{kg}$ are left $1\text{m}$ apart on a smooth frictionless surface. What is the resulting acceleration of the blocks? $\left[2\text{marks}\right]$